The Statistics of Microwave Popcorn 

11:00 The pdf is the derivative of the cdf, so that's the inverse function theorem on the cdf (1 / f'(f^-1(p))), giving you the derivative of the inverse of the cdf, the inverse cdf is the quantile so this is the quantile density function (qdf)

I like how something useless as gravitational waves helped humanity understand more meaningful stuff such as popcorn pop's

I like how you connect so many fields of science just in one topic

I wonder if the popcorn companies looked into this same kind of statistical analysis, or if they arrived at "wait 1-2 seconds between pops to pull out" as a gut check, from years of experience making popcorn. Great video, and the first of yours that I've seen. I'm definitely subscribing

Many microwave ovens have a "popcorn" button, yet most microwave popcorn instructions will advise against using it. This is because generally, that option is just a fixed timer, which will often burn your popcorn. BUT some microwaves instead detect the steam released from the popcorn, and dynamically adjust the time that they cook the popcorn, to avoid burning it. This is very cool and lets you walk away from your microwave without fear of burning your snack!

I've just started my first course on data analytics and I could see this video being shown to all students as a way to show the applications (and I'll definitely recommend it to others). Amazing work!

I lobe that this video does a ton of math and experimentation and detailed exploration of the science of popping corn, and then concludes with "Yep, the instructions are right." More seriously, confirmation studies are far too uncommon in science. This sort of thing should happen more often, not just on RU-vid, but also in academia. Brilliant.

This channel has been a fantastic discovery because it's someone with my exact intersection of niche interests and hobbies, but importantly also the drive and energy to actually go through with the crazy ideas like mathematically model popcorn intervals in code. I live vicariously through this content.

Here's another tip! Shake the bag shortly after you notice the popping slowing down, helps spread the heat, just be careful not to burn yourself. I get noticeably less unpopped kernels that way.

Fun Fact: You can make delicious microwave popcorn that is CHEAPER and SOFT (doesn't get stuck between your teeth). Simply buy popcorn corn, put it in a large glass bowl (only enough to cover the bottom of bowl), add a thin layer of water (very little, only covering the kernels halfway), place a glass dish on top of bowl. Microwave at highest potency until just before popping sound stops (timing is finicky and can be tricky, might burn a few times before you get it just right).

Man, this channel is popping off! Another great explanation, which covered a variety of topics.. Definitely one the best channels to come about in the last few months... Keep up the good work, Physics Bird.

Man literally proved that popcorn popping slowing down in a microwave means that most of the kernels have already opened, using complex mathematical analysis. I love this channel.

This channel just randomly popped up and started prolifically making some of the best science videos I’ve seen. They’re so nice to watch.

The use of the Central limit theorem here is not exact, it's correct for sums (or averages) of variables coming from the same distribution, so not for sum of the different things that cause popcorn to pop at a certain time. I'd say the reason that you should expect pops to be distributed normally is because you are averaging over many kernels that might pop but not because you are summing over the reasons. regardless, I really like the channel and I'm happy to see it's really gaining attention.

If you want more of the kernels to pop, unfold the bag and use your fingers to rip the adhesive on the bottom left and bottom right of the bag, this allows the bottom of the bag to expand more as the popcorn pops, and because there's more space, the popped kernels have more time before they burn, thus allowing the unpopped kernels more time to pop.

Great video! Just one small detail, the central limit theorem requires that the variables are independent and have the same distribution for their sum to converge to a gaussian

The thing I love about science and engineering is that the practical application of mathematical concepts, even to seemingly random situations like this, can give insights that allow objects and processes to be further refined and optimized to improve our daily lives. I’m Glad the algorithm recommended this video.

This channel is way too good for how few videos you've made. I really love the way you attack the whole problem, incorporating as many flavors of physics as neccessary to get to a satisfying explanation. I'm a fluid dynamicist, so I especially like when you dip into the wonderfully confusing world of fluids, but really all the physics explored in these vids are interesting and described exceedingly well. Also the art is great. Just all around excellent work!

That’s pretty cool,it seems worth it to count. That 10% that’s unpopable always made it feel like there wasn’t really a right way so long as it didn’t burn

The algorithm recommended this video to me, and I decided to watch as I washed some dishes. All the popcorn talk made me want to go microwave a bag, then I wound up watching two more of your videos. Great content! I love your narration style and your simple explanations of difficult concepts that I would have loved when I was struggling through 100-level physics!

I literally subscribed like 2 days ago and at the same time have started making microwave popcorn more frequently. This video is for ME

I am a student in economics at the ENS and I have in my study plan Statistical Physics, I am loving the patterns that repeat themselves for all these different phenomenon, the fact that aggregation of these simple events gives birth to complex system approaches gives me the idea that the scientific method talks in the same way, we are only separated because every human is limited

Great videos on your channel. Explaining a topic clearly and completely, without dumbing it down, is a real skill. Doing it in a way that turns out to be interesting, educational, and understanding is rare indeed. Keep up the great work!

I can't believe I only recently discovered this channel. What hard hitting science. I pop my popcorn methodically as well

Some years ago I've discussed with a Matemathician and a Physicist friend the popcorn topic... I asume the "popping" as a logístic function depending on time, comparing the process of popping with a second order transition phase. The density of "poppings" in the microwave time Interval must obey a probability distribution, althoug at beginig my Friends laughed at me they concluded it would be interesting to do some experimentation and get the data... Sadly it was a tough moment of My lfe and I had not resources (time, money, entusiasm) to do this research for fun. After all this years I've learned new concepts and realized My idea for popcorn experiment translated into a logístic map may show interesting aspects of dinámics and criticality... Wee know that logístic function has proven to be more than the eye catch ;) PD great channel, great content! ... I. Suscribed Yesterday after watching your vídeo on why we like Jazz.

I’m really amazed by how many different concepts are condensed into one video. Not only do you spot the similarities between them, but also do the math and draw great conclusions! You need way more subs

Glad to see you growing so much, Mr. Birds! You deserve this so much -- your videos have great production quality and are fascinating.

Brilliant video! Live the style of presentation, the homemade scientific experiment and the opportunity to learn a whole lot of different concepts and ideas on one video. Glad I subscribed 😊

This channel needs to blow up more - so here I am in the comments. The content is unmatched. Great stuff!

I love the nerdiness of how you pop your popcorn. It is unbelievably cute :) Another great video!

I just got started watching this video but it raises a good productive point about instructions, whether on microwave things or other products. Very important!

this is by far my favorite youtube channel! Covers topics I love with enough rigor and topics I am interested in an easy to understand way ❤❤❤

Great video I really enjoyed it! However 4:30 is not what the Central Limit Theorem says, and it leads to an unfair assumption that the the time it takes for a popcorn to pop is normal. The CLT says that the sum of i.i.d random variables tends to a normal distribution as the number of RVs increases. The CLT really doesn't say anything about adding distributions in general. The example with the dice illustrates the CLT well. However 4:30 what you're doing is adding a simply adding distributions together (a small number at that), the problem here is the distributions are definitely not identically distributed (if we assume the distributions for strength, volume etc. are represented by the drawings you've shown then you can clearly see that they aren't identically distributed). The reason why it works for the dice example is 1) because for any die there's a 1/6 chance of rolling each number, so the each dice throw is identically distributed, and 2) they're clearly independent and also you in the video you show what happens in the limit (i.e involving a large number of dice). Applied to popcorn popping times the CLT would say something like: if you take a bunch of popcorn and pop them, and add up the time it takes each one to pop, then "the sum of the time it takes for each popcorn to pop" follows a normal distribution. Note that it importantly doesn't say anything about the underlying distribution of the time it takes a single popcorn to pop.

Dude you just made so much of my time in college start clicking together. These aren’t just abstract concepts…they’re tools! Tools that can be used to do awesome things!

Rarely comment, but I have to say that this video is outstanding! The style, the pace, the wit, it's almost perfect! Please make more!!!

This short video made me spend so, so much extra time reading up on concepts and honestly is absolutely amazing

The normality argument (4:34) seemed very suspicious to me. You could use the same argument (that a random variable has many contributing factors) to show that, for instance, mealtimes are normally distributed throughout the day. To apply the CLT, you have to believe that each independent factor has a negligible effect on the sum.

Really cool video! PS: Could you share the popcorn audio and the pop times? I'd love to play around with the data.

the amount of detail is astounding, i love it

I just found this channel last night and watched all the videos back-to-back, and as soon as I’m done a new video comes out. I’ll take that as a sign that I should stick around and subscribe lol

That was very cool, would love to know more on the subject. I study chemistry and found your statistics very interesting

For those who hate having extra kernels, before putting the bag in the microwave flatten the seeds evenly throughout the bag so they're not clumped up If you just tear off the plastic and pop it in, it will be too clumpy and won't cook evenly. I always spread out the kernels till everything is flat and I only get like 3-4 kernals.

Your videos are amazing. Thank you for your time and research. I am sure there is a lot you do behind the scenes, and I appreciate your time!

I did a project for university where we needed to find a wolf's howl in a large dataset and use the time-delay between different microphones to triangulate it's position, and we used the exact same method of detecting signals as you did! We did however not use the [-1,1] trick for the moving average to find the starting time so it gave us a lot of headaches! You just solved my internal conflict for not finding a short/satisfying solution for that problem. Thanks!

I genuinely love the fact you straight up count each time you pop popcorn lol. For me I figured out years ago that 2:25 in my microwave gets it pretty perfect and just go do something else while I wait on it. 2 different mindsets, the "good enough" mindset and the "there has to be a perfect formula for this".

late night searching of youtube never disappoints, your channel was just recommended and i watched all your videos and they are all amazing, keep up the great content, the way you explain everything in all your videos is amazing and so well said. keep it up

I always look forward to these videos. So many subjects condensed into something easy to follow

Thank you RU-vid for this amazing suggestion. Loved the video! Gonna rush to watch the rest of the channel now.

I LOVE this video. I've thought about this sort of analysis every time I've made microwave popcorn and always wondered why popcorn companies don't make an analysis app to help with achieving optimal popcorn.

Brother, your channel is a gem!! Don't stop doing what you're doing!

Wow! It takes a lot of skill to make educational content that is genuinely informative and useful, while remaining accessible and engaging for all audiences. Multi-objective optimization really is one of your strong suits 😉.

"So before we can explain how long you should microwave your popcorn, _let me explain astrophysics."_ Yep. Found the reputable and needlessly in depth source. _Bless you._

I'm amazed at how creative you've been at sneaking in signal processing into a video.

just watched all of your vids in this one sitting, you make really good content and i cant wait for more

One of the best physics videos I've seen in a long time. The work you put in and showed was covered in great detail. Nerds rejoice! A new RU-vid Physics Saint has cometh!

I love the sense of curiosity from all of your videos. Your content inspires me to start projects of my own! Thanks!

Great video and touches on the topic of the dichotomy between closed "black box" system and environment in which many systems such as complex, quantum and unobservable systems fall under. The thing that always blows my mind is how complexity, in the signal space which can be represented as the networks graph space, always seems to emerge here. Once you go down this rabbit hole it never ceases to amaze how much deep structures are hidden and find commonality across the scales. Something about the interplay between the physical laws that govern heat transfer and percolation in a bag of popcorn and similar effects in Bose-Einstein condensates give me big "theory of everything" vibes!

Wonderful video! I’m halfway through a physics degree and I love seeing some of the concepts I come across in class put to good use

What a gem of a channel

What a world we live in. To put so much scientific knowledge to understand the mundane. Truly, we are blessed

Finally, an actual application of statistical analysis! After working with ML for a few years and feeling that I'm only using it as a black box is refreshing seeing someone use actual statistics to solve a problem. Can't wait to see the rest of your videos :)

This channel is becoming my favorite, very enjoyable videos and kudos to the curator for making the whole thing investing and entertaining

It is really clever how they managed to turn a fairly complex problem into instructions this simple.

Another wonderful exploration prompted by curiosity! Hope your birds have a nice day!

i love that the internet has become a place where you can watch a well produced in depth video about microwave popcorn. great video

6:38 you can pinpoint the precise moment I fell in love with you and your channel and instantly subscribed

I'm so glad I found this channel, such a hidden gem.

Also worth mentioning your great graphics skills which helps present complicated statistical theories in an enjoyable manner. Good job!

Another great video, well done! You’ve become one of my favourite channels.

You have the potential to rival Minute Physics and Minute Earth! Such great contents connecting so many fields together! Thank you so much for the great work!

Awesome! You're coverage of the signal processing tricks has won my subscription good sir. The bit about convolution with the [-1 1] was a new trick for me, so thanks! More awesome applied math and science videos please!

Dude. Anybody that can connect popcorn popping and black holes merging has earned my subscription.

I heard your voice and immediately subscribed. I don't know what it is about your voice but it's very lovely and fills me with joy.

this channel is so underappreciated

This video is fantastic! Helps frame some other concepts quite well, more to be learned here than fluffy corn balls being birthed in a small wave machine.

I obssess over this as well! This channel is really awesome

The amount of work to get the same answer is beautiful. More content like this.

What a fabulous circle that was just to come back to where you started!

Top work, have found your channel recently and it doesn’t miss for interesting physics. Keep it up!

I've mastered the art of microwaving popcorn, I have 5 to 10 kernels MAXIMUM in the bag after I'm done with it!

i'm so happy that this video was recomended to me, i love this channel

Another brilliant video! Love the channel, and a follow up point: if you want maximum kernels popped, make it on the stove the old fashioned way. I’ve been enjoying the luxury of all kernels popped for years now with a little olive oil, butter, a saucepan, and a bag or organic popcorn kernels which you can buy in bulk at the store. Add a dash of sea salt and you’re in heaven.

thank you for scientifically validating the instructions

This was a great video. Really shows you how important and applicable statistics are. Thank you

I absolutely adore the interdisciplinary education aspect of this channel! So many disparate fields of math and science working in a lovely tandem!

I love this! We often forget that physics governs even the most mundane thing in our lives. Thank you for reminding me :)

I'm teaching statistics for engineers right now, and about to start explaining the Gaussian distribution next week. So your video comes out handy for the occasion, as a good example of the Central Limit Theorem that relies on every day experience, not on some arcane mathematical function shuffling. In any case I've enjoyed the experimental approach a lot; I'm also an occasional amateur home scientist. Thanks a lot.

Never knew I could be so invested about a popcorn video. You pop off queen 🥲

This video was absolutely brilliant

I never knew I would need this but I am glad I encountered it and it was beautiful. Thank you sir!

wow the signal convolution just solved an edge detection issue i was having with a problem and i actually have leads to research more as a result, thanks

Great video! I've found that spreading out the kernels in the package a bit before microwaving reduces the standard deviation in pop time, making it easier to get a higher % of kernels popped without burning your popcorn.

OMG I just got done doing my Discrete Signals and Systems homework and I was finally able to eat dinner and watch RU-vid. But, then I heard the word Convolution and realized I could not escape my classes. Great video I love your channel. You make learning fun!

Amazing video and also amazing channel, explanations are clear and your sense of humor is great. Keep up the good work.

What an amazing video, I am blown away, thank you so much

this is the best channel on youtube, never change!

All the science and you referenced ‘the lick’. Great video.

I love this channel and I'm not even 3 mins in, it's just the vibe, I want to listen

This is one of the best videos I have ever seen. Instant sub

my new favorite youtube channel thank you!